5
QuizMultiple Choice

Rational Functions — Test

Question 5 • Algebra II

How can Ari simplify the following expression? the fraction with numerator the fraction with numerator 5 and denominator A minus 3 minus 4 and denominator 2 plus the fraction with numerator 1 and denominator A minus 3

Answer
A
Divide the numerator and the denominator by A minus 3 . Then divide the numerator by the denominator.
B
Write the numerator and denominator with a common denominator. Then divide the numerator by the denominator. To do this, multiply the numerator by the reciprocal of the denominator.
C
Write the numerator and denominator with a common denominator. Then divide the numerator by the denominator. To do this, multiply the numerators and multiply the denominators.
D
Divide the numerator and the denominator by A minus 3 . Then simplify the numerator and simplify the denominator.

Explanation

The expression is a complex fraction: its numerator is 5/(A − 3) − 4, and its denominator is 2 + 1/(A − 3). First, rewrite each of those parts using a common denominator. Then divide the resulting numerator by the resulting denominator by multiplying by the denominator’s reciprocal. Multiplying the numerators and multiplying the denominators, as choice C suggests, is not how division of fractions works.

AI-written and checked against the verified answer.

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